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There is already a question on this site comparing the number of IPv6 addresses to the number of grains of sand on earth, but my question is different.

There is a famous quote that many in networking have heard before:

"It isn't remotely likely that we’ll run out of IPV6 addresses at any time in the future. We could assign an IPv6 address to every atom on the surface of the Earth, and still have enough addresses left to do another 100+ earths."

Is this statement is correct?

Because according to Wolfram, there are 1x10^50 atoms on earth.

While the total number of IPv6 addresses equals 3.4×10^38

Can IPv6 accommodate the atoms of 100+ more earths?

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Sufiyan Ghori
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    Note the difference between the number of atoms in the Earth, and the number of atoms on the surface of the Earth. – jmite Jul 24 '14 at 19:20
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    http://xkcd.com/865/ – dmckee --- ex-moderator kitten Jul 24 '14 at 19:24
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    Besides the "number of atoms" the other part is "the number of IPv6 addresses". Currently (and it is not easy to change) the "2000::/3" prefix is the only one for routable global unicast addresses. And considering the fact that even for dialup sites it is tried to assign at minimum a /64. So there are "only" 2^61 = 2.3x10^18 sites if no address space is wasted (which it is). –  Jul 25 '14 at 01:13
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    @eckes Actually, at the ISP I work for we've decided to give out /48s because we're basically more worried about the possible eventual size of the routing table than we are about running out of address space to allocate. – Shadur Jul 25 '14 at 04:53
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    it's about 1 mole of addresses per square yard of the earth's surface (http://cnx.org/content/m12460/latest) – warren Jul 25 '14 at 19:32

1 Answers1

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You misinterpreted the quote.

The number of atoms on the surface of earth(1) is 1.26 x 1034 and the number of atoms on earth is 1.33 x 1050 (does not concern us here).

The total number of IPV6 that we can assign is: 3.4 x 1038.

3.4 x 1038 > 1.26 x 1034.

The following is true and here is the full quote for you:

BUT, there are 6-billion people on the planet, so if everyone was assigned just one IP address, we’d run out and leave 1/3rd of the world without IP addresses. So they invented IPV6, a 128-bit value, which is 16-bytes long. Since they had to identify this to distinguish it from 4-byte values, the 1st byte has a 1-byte value that was never used in the 1st byte of the original 32-bit addresses. So that leaves 2120 possible IP addresses using IPV6. How big is that? Well, several web sites say there are 1.33 x 1050 atoms in the earth. That’s way bigger than 2120. But to make it come closer, I computed the number of atoms on the surface of the earth. That turns out to be 1.26 x 1034 atoms. 2120 is 1.33 x 1036, which is still bigger by 105 times. So we could assign an IPV6 address to EVERY ATOM ON THE SURFACE OF THE EARTH, and still have enough addresses left to do another 100+ earths. It isn’t remotely likely that we’ll run out of IPV6 addresses at any time in the future.

(1) The number of atoms on the surface = 4πr2 x (1/2a)2. Planet's radius = 6378km, mean atomic radius of the common stuff averages about 100pm. Total= 1.27*1034 . calculated by paul (see the comments).

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George Chalhoub
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    IPv4 and IPv6 are distinguished by the IP version field and (optionally) a field in the encapsulating frame (e.g. Ethernet frame type), not by using magic numbers inside the address field. – Simon Richter Jul 25 '14 at 07:22
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    Another comparison: there are currently 7 billion people on Earth (7*10^9). There are estimated to be 300 billion stars in the galaxy (3*10^11). There are estimated to be 500 billion galaxies (5*10^11). If every galaxy has 300B stars, and every star has 1 planet with 7B intelligent beings, there are enough IPv6 addresses to give each of those beings 10 devices, AND do the same for another 10,000 or so universes. – Nzall Jul 25 '14 at 10:01
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    I'm extremely skeptical/"call bullshit" on the calculation for the number of atoms on the surface of the Earth. I wonder if that's a tangent or not as it relates to this question. – HopelessN00b Jul 25 '14 at 13:33
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    @HopelessN00b Since the "surface of the earth" is not particularly well-defined. I'm sure they probably doctored the numbers to fit the point. Of course to me, if you just say 128-bit address is enough to convince me. There's certainly a buttload of address space. – Cruncher Jul 25 '14 at 13:40
  • @HopelessN00b their calculation is calling approximately 1 10000000000000000th of the earth as the "surface". An apple is probably more than 1 1000th skin. – Cruncher Jul 25 '14 at 13:43
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    Number of atoms on the surface = 4πr^2 * (1/(2a))^2. Planet's radius = 6378km, mean atomic radius of the common stuff averages about 100pm. Total: 1.27*10^34. Close enough. Surface != crust. – paul Jul 25 '14 at 14:16
  • Assume each atom in the earth is a cube and there is no space in between atoms. Call the length of one side of this cube x. Using x as our unit we get. Earth's volume = 1.33*10^50 * x^3 = 4/3*pi*r^3 => r = 3.166*10^16 * x Earth's surface = 4*pi*r^2 = 1.26*10^34 * x^2 – Tesseract Jul 25 '14 at 15:28
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    @paul That would be the case if the Earth was perfectly spherical, and would be a reasonable estimate if the earth was even reasonably spherical. However, every valley and peak adds to the surface area, and the earth is ovoid to begin with... and 2/3 covered by water, all of which will skew the surface area higher compared to a perfect sphere, to a counter-intuitively large degree. Add the unkownable distance between atoms to the equation, and ... while that number may be reasonable for an Earth-sized sphere, it could be many orders of magnitude off for the actual Earth. – HopelessN00b Jul 25 '14 at 18:52
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    @HopelessN00b don't nit-pick details on what is very obviously a broad analogy. It just annoys everyone. – paul Jul 26 '14 at 01:54
  • So the argument is that the number of atoms *in a 1 atom thick layer* is ~10^34 ? Have I got that right? – matt_black Aug 13 '14 at 14:35
  • As pointed out in Sandeep's [answer that should have been a comment](http://skeptics.stackexchange.com/a/37818/35250), you've misquoted the source. It says, correctly, that the factor is 105 times, not 10^5. – phoog Mar 31 '17 at 19:21